Numerical methods and parameter estimation of a structured population model with discrete events in the life history

We consider two numerical methods for the solution of a physiologically str uctured population (PSP) model with multiple life stages and discrete event reproduction. The model describes the dynamic behaviour of a predator-prey system consisting of rotifers predating on algae. The nitrate limited alga l prey population is modelled unstructured and described by an ordinary dif ferential equation (ODE). The formulation of the rotifer dynamics is based on a simple physiological model for their two life stages, the egg and the adult stage. An egg is produced when an energy buffer reaches a threshold v alue. The governing equations are coupled partial differential equations (P DE) with initial and boundary conditions. The population models together wi th the equation for the dynamics of the nutrient result in a chemostat mode l. Experimental data are used to estimate the model parameters. The results obtained with the explicit finite difference (FD) technique compare well w ith those of the Escalator Boxcar Train (EBT) method. This justifies the us e of the fast FD method for the parameter estimation, a procedure which inv olves repeated solution of the model equations. (C) 2000 Academic Press.